clicking “check repository” doesn’t initiate the svn search, you may not have a languages directory. Check your site’s folders. There needs to be a writable languages directory located at /wp-content/languages/ otherwise the process fails

This plugin appears to be in serious need of support. As far as I can tell, on my WordPress 3.9.1 test installation, none of the javascript necessary to handle clicks on “check repository” and handle the download process appears to be getting included in the admin page.

After a frustrating few hours of trying to debug this, it seems the author has hooked that javascript onto ‘admin_head’, which would – at the very least – unnecessarily load that javascript into every admin page, not just the settings page for this plugin. That could be causing no end of conflicts with other plugins. It may not be the entire reason for the issue, but for me, clicking “check repository” does absolutely nothing.